Optimization Strategies in Complex Systems

We consider a class of combinatorial optimization problems that emerge in a variety of domains among which: condensed matter physics, theory of financial risks, error correcting codes in information transmissions, molecular and protein conformation, image restoration. We show the performances of two algorithms, the "greedy'' (quick decrease along the gradient) and the "reluctant'' (slow decrease close to the level curves) as well as those of a "stochastic convex interpolation'' of the two.Concepts like the average relaxation time and the wideness of theattraction basin are analyzed and their system size dependenceillustrated.